The Causal Marginal Polytope for Bounding Treatment Effects
- URL: http://arxiv.org/abs/2202.13851v1
- Date: Mon, 28 Feb 2022 15:08:22 GMT
- Title: The Causal Marginal Polytope for Bounding Treatment Effects
- Authors: Jakob Zeitler, Ricardo Silva
- Abstract summary: We propose a novel way to identify causal effects without constructing a global causal model.
We enforce compatibility between marginals of a causal model and data, without constructing a global causal model.
We call this collection of locally consistent marginals the causal marginal polytope.
- Score: 9.196779204457059
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: Due to unmeasured confounding, it is often not possible to identify causal
effects from a postulated model. Nevertheless, we can ask for partial
identification, which usually boils down to finding upper and lower bounds of a
causal quantity of interest derived from all solutions compatible with the
encoded structural assumptions. One appealing way to derive such bounds is by
casting it in terms of a constrained optimization method that searches over all
causal models compatible with evidence, as introduced in the classic work of
Balke and Pearl (1994) for discrete data. Although by construction this
guarantees tight bounds, it poses a formidable computational challenge. To cope
with this issue, alternatives include algorithms that are not guaranteed to be
tight, or by introducing restrictions on the class of models. In this paper, we
introduce a novel alternative: inspired by ideas coming from belief
propagation, we enforce compatibility between marginals of a causal model and
data, without constructing a global causal model. We call this collection of
locally consistent marginals the causal marginal polytope. As global
independence constraints disappear when considering small dimensional tractable
marginals, this also leads to a rethinking of how to elicit and express causal
knowledge. We provide an explicit algorithm and implementation of this idea,
and assess its practicality with numerical experiments.
Related papers
- Effective Bayesian Causal Inference via Structural Marginalisation and Autoregressive Orders [16.682775063684907]
We decompose the structure learning problem into inferring causal order and a parent set for each variable given a causal order.
Our method yields state-of-the-art in structure learning on simulated non-linear additive noise benchmarks with scale-free and Erdos-Renyi graph structures.
arXiv Detail & Related papers (2024-02-22T18:39:24Z) - Revisiting Deep Generalized Canonical Correlation Analysis [30.389620125859356]
Canonical correlation analysis is a classic method for discovering latent co-variation that underpins two or more observed random vectors.
Several extensions and variations of CCA have been proposed that have strengthened our capabilities in terms of revealing common random factors from multiview datasets.
In this work, we first revisit the most recent deterministic extensions of deep CCA and highlight the strengths and limitations of these state-of-the-art methods.
arXiv Detail & Related papers (2023-12-20T22:15:10Z) - Invariant Causal Set Covering Machines [64.86459157191346]
Rule-based models, such as decision trees, appeal to practitioners due to their interpretable nature.
However, the learning algorithms that produce such models are often vulnerable to spurious associations and thus, they are not guaranteed to extract causally-relevant insights.
We propose Invariant Causal Set Covering Machines, an extension of the classical Set Covering Machine algorithm for conjunctions/disjunctions of binary-valued rules that provably avoids spurious associations.
arXiv Detail & Related papers (2023-06-07T20:52:01Z) - Active Bayesian Causal Inference [72.70593653185078]
We propose Active Bayesian Causal Inference (ABCI), a fully-Bayesian active learning framework for integrated causal discovery and reasoning.
ABCI jointly infers a posterior over causal models and queries of interest.
We show that our approach is more data-efficient than several baselines that only focus on learning the full causal graph.
arXiv Detail & Related papers (2022-06-04T22:38:57Z) - Bayesian Model Selection, the Marginal Likelihood, and Generalization [49.19092837058752]
We first revisit the appealing properties of the marginal likelihood for learning constraints and hypothesis testing.
We show how marginal likelihood can be negatively correlated with generalization, with implications for neural architecture search.
We also re-examine the connection between the marginal likelihood and PAC-Bayes bounds and use this connection to further elucidate the shortcomings of the marginal likelihood for model selection.
arXiv Detail & Related papers (2022-02-23T18:38:16Z) - Partial Counterfactual Identification from Observational and
Experimental Data [83.798237968683]
We develop effective Monte Carlo algorithms to approximate the optimal bounds from an arbitrary combination of observational and experimental data.
Our algorithms are validated extensively on synthetic and real-world datasets.
arXiv Detail & Related papers (2021-10-12T02:21:30Z) - Estimation of Bivariate Structural Causal Models by Variational Gaussian
Process Regression Under Likelihoods Parametrised by Normalising Flows [74.85071867225533]
Causal mechanisms can be described by structural causal models.
One major drawback of state-of-the-art artificial intelligence is its lack of explainability.
arXiv Detail & Related papers (2021-09-06T14:52:58Z) - Algorithmic Recourse in Partially and Fully Confounded Settings Through
Bounding Counterfactual Effects [0.6299766708197883]
Algorithmic recourse aims to provide actionable recommendations to individuals to obtain a more favourable outcome from an automated decision-making system.
Existing methods compute the effect of recourse actions using a causal model learnt from data under the assumption of no hidden confounding and modelling assumptions such as additive noise.
We propose an alternative approach for discrete random variables which relaxes these assumptions and allows for unobserved confounding and arbitrary structural equations.
arXiv Detail & Related papers (2021-06-22T15:07:49Z) - Causal Expectation-Maximisation [70.45873402967297]
We show that causal inference is NP-hard even in models characterised by polytree-shaped graphs.
We introduce the causal EM algorithm to reconstruct the uncertainty about the latent variables from data about categorical manifest variables.
We argue that there appears to be an unnoticed limitation to the trending idea that counterfactual bounds can often be computed without knowledge of the structural equations.
arXiv Detail & Related papers (2020-11-04T10:25:13Z) - A Class of Algorithms for General Instrumental Variable Models [29.558215059892206]
Causal treatment effect estimation is a key problem that arises in a variety of real-world settings.
We provide a method for causal effect bounding in continuous distributions.
arXiv Detail & Related papers (2020-06-11T12:32:24Z)
This list is automatically generated from the titles and abstracts of the papers in this site.
This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.